Perovskites down to the monolayer limit have emerged and have attracted increased interest due to their two-dimensional nature with potentially novel physical properties. Here, we investigate the phonon transport in the oxide perovskite ${\mathrm{SrTiO}}_{3}$ with thicknesses from the monolayer limit to 10 nm by constructing an accurate first-principles machine-learning potential and combining it with the Boltzmann transport equation and homogeneous nonequilibrium molecular dynamics simulations. Compared to its bulk counterpart, the phonon dispersion relation of monolayer ${\mathrm{SrTiO}}_{3}$ is insensitive to temperature, and the calculated in-plane thermal conductivity of monolayer ${\mathrm{SrTiO}}_{3}$ is much larger than that of bulk ${\mathrm{SrTiO}}_{3}$, which mainly results from the unique out-of-plane atomic vibrations in monolayer ${\mathrm{SrTiO}}_{3}$. The thermal conductivity of ${\mathrm{SrTiO}}_{3}$ thin film first decreases and then approaches the bulk value as thickness increases from the monolayer limit to 10 nm. The hardening of the out-of-plane acoustic phonon branch and the transition of low-frequency optical phonons can explain the observed trend in thermal conductivity transitions. Our study demonstrates that monolayer ${\mathrm{SrTiO}}_{3}$ has a higher thermal conductivity than its bulk counterpart with covalent bonds at the first-principles level of accuracy, and dimension reduction has a weak inhibition on phonon transport in freestanding atomically smooth ${\mathrm{SrTiO}}_{3}$ thin films, which furthers the understanding of phonon transport in two-dimensional perovskite thin films.